Results 1 to 4 of 4

Math Help - Circle question

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    14

    Circle question

    If you draw a circle inside a square and the circle fits exactly inside the square, how many percents of the square does the circle cover?

    I need an easy and understandable formula and the result too if possible. Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Shandy View Post
    If you draw a circle inside a square and the circle fits exactly inside the square, how many percents of the square does the circle cover?

    I need an easy and understandable formula and the result too if possible. Thanks!
    A circle inside a square of sidelength x has a radius of \frac{x}{2}.

    Substitute this data into the usual formulae for the area of a square and the area of a circle. Then calculate the percentage of area covered.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    14

    Correct or not?

    Is my result correct or not?

    A perfectly fit circle inside a square covers 80% of the square.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Quote Originally Posted by Shandy View Post
    Is my result correct or not?

    A perfectly fit circle inside a square covers 80% of the square.
    If the radius of the circle is r, then the sides of the square are of length 2r.

    So the fraction of the square that is covered is \frac{\pi r^2}{(2r)^2} = \frac{\pi}{4}, which is about 0.78, so you are about right.

    Grandad

    Last edited by mr fantastic; February 5th 2009 at 03:09 AM. Reason: No edit - just flagging the reply as having been moved from another thread.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A Circle Question.
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: February 14th 2011, 01:19 PM
  2. [SOLVED] Circle question.
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 9th 2011, 06:07 PM
  3. Question about circle?
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 7th 2010, 06:29 AM
  4. circle question
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 8th 2009, 09:05 AM
  5. circle question
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: December 10th 2008, 09:52 AM

Search Tags


/mathhelpforum @mathhelpforum